Relationships Between the Bergman Kernels of Hartogs Domains and Their Base
Complex Variables
2024-06-25 v2
Abstract
We explore the relationship between the Bergman kernel of a Hartogs domain and weighted Bergman kernels over its base domain. In particular we develop a representation of the Bergman kernel of a Hartogs domain as a series involving weighted Bergman kernels over its base, as well as a "transformation" formula for some weighted Bergman kernels. Other relationships of this type are presented.
Cite
@article{arxiv.2208.14291,
title = {Relationships Between the Bergman Kernels of Hartogs Domains and Their Base},
author = {Blake J. Boudreaux},
journal= {arXiv preprint arXiv:2208.14291},
year = {2024}
}